1. Field of the Invention
This invention relates to an interpolation processing method and apparatus for an image signal.
2. Description of the Prior Art
Techniques for photoelectrically reading out an image, which has been recorded on a photographic film, in order to obtain an image signal, carrying out appropriate image processing on the image signal, and then reproducing a visible image by use of the processed image signal have heretofore been known in various fields.
Also, it has been proposed to use stimulable phosphors in radiation image recording and reproducing systems. Specifically, a radiation image of an object, such as a human body, is recorded on a sheet provided with a layer of the stimulable phosphor (hereinafter referred to as a stimulable phosphor sheet). The stimulable phosphor sheet, on which the radiation image has been stored, is then exposed to stimulating rays, such as a laser beam, which cause it to emit light in proportion to the amount of energy stored thereon during its exposure to the radiation. The light emitted by the stimulable phosphor sheet, upon stimulation thereof, is photoelectrically detected and converted into an electric image signal. The image signal is then processed and used for the reproduction of the radiation image of the object as a visible image on a recording material, such as photographic material, or on a display device, such as a cathode ray tube (CRT) display device. Radiation image recording and reproducing systems, which use stimulable phosphor sheets, are advantageous over conventional radiography using silver halide photographic materials, in that images can be recorded even when the energy intensity of the radiation, to which the stimulable phosphor sheet is exposed, varies over a wide range.
In image recording and reproducing systems, in which an image signal is obtained in the manner described above and a visible image is reproduced from the image signal, in cases where the region of interest in the visible image is to be viewed in more detail, the region of interest is often enlarged and reproduced. In such cases, if the enlargement of the image size is carried out such that the number of the image signal components of the image signal representing the enlarged image may be identical with the number of the image signal components of the original image signal representing the original image, the sharpness of the enlarged image will be recognized to be lower than the sharpness of the original image due to the visual characteristics of persons. Therefore, if the image is merely enlarged and reproduced, an enlarged image having a high sharpness cannot be obtained, and the details of the image cannot be viewed accurately.
In order for the aforesaid problems to be eliminated, a predetermined interpolation processing may be carried out on the original image signal, which has been obtained by reading out an original image, and an interpolation image signal, which is a secondary image signal and is made up of a number of image signal components different from that of the original image signal, may thereby be formed. Specifically, in cases where an enlarged image is to be reproduced, an interpolation image signal, which is made up of a number of image signal components larger than that of the original image signal, may be formed from the interpolating operation. A visible image may then be reproduced from the interpolation image signal. In this manner, the sharpness of the enlarged image can be prevented from becoming low.
As the interpolation processing carried out on image signals, various methods have heretofore been proposed. Among such methods, the processing using third-order spline interpolating functions is popular. With the interpolation processing using the third-order spline interpolating functions, digital original image signal components (Y.sub.k), which correspond to each set of two adjacent picture elements, are connected by a third-order function {f.sub.k }. (The region between the two adjacent picture elements in each set is herein referred to as a section.) Also, the value of f.sub.k corresponding to a position, at which an interpolation point (i.e., a point that is to be inserted) is set, (i.e., a setting position in each section) is taken as the value of the interpolated image signal component.
The interpolating operations, which pass through the original image signal in the manner described above, are the interpolation processing capable of yielding an image having a comparatively high sharpness. As the interpolating functions for such interpolation processing, cubic spline interpolating functions, and the like, are known. How the cubic spline interpolating functions operate will be described hereinbelow.
FIG. 2 is an explanatory graph showing how interpolated image signal components are obtained with a cubic spline interpolation processing from original image signal components, which are sampled with a period of an equal interval and represent sampling points (picture elements) arrayed in one direction. As illustrated in FIG. 2, the image signal components (the original image signal components), which have been detected as digital signal components from an original image and represent a series of picture elements X.sub.k-2, X.sub.k-1, X.sub.k, X.sub.k+1, X.sub.k+2, . . . , are respectively represented by Y.sub.k-2, Y.sub.k-1, Y.sub.k, Y.sub.k+1, Y.sub.k+2, . . . A third-order spline interpolating function is set for each of sections X.sub.k-2 .about.X.sub.k-1, X.sub.k-1 .about.X.sub.k, X.sub.k .about.X.sub.k+1, and X.sub.k+1 .about.X.sub.k+2. The spline interpolating functions corresponding to the respective sections are represented by f.sub.k-2, f.sub.k-1, f.sub.k, f.sub.k+1, and f.sub.k+2. The interpolating functions are the third-order functions, in which the position in each section serves as a variable.
Firstly, how the interpolating operation is carried out when an interpolation point X.sub.p falls within the section X.sub.k .about.X.sub.k+1 will be described hereinbelow. The spline interpolating function f.sub.k corresponding to the section X.sub.k .about.X.sub.k+1 is represented by Formula (1) shown below. EQU f.sub.k (x)=A.sub.k x.sup.3 +B.sub.k x.sup.2 +C.sub.k x+D.sub.k ( 1)
In the cubic spline interpolating function f.sub.k, it is necessary that the function passes through the picture elements of the original image (i.e., the original sampling points), and that the first-order differential coefficient of the function is continuous between adjacent sections. Also, it is necessary for the first-order differential coefficient at the picture element X.sub.k to satisfy the condition with respect to the picture elements X.sub.k-1 and X.sub.k+1, which are located before and after the picture element X.sub.k, in that the first-order differential coefficient at the picture element X.sub.k should coincide with the gradient (Y.sub.k+1 -Y.sub.k-1)/(X.sub.k+1 -X.sub.k-1) of the image signal components Y.sub.k-1 and Y.sub.k+1 representing the picture elements X.sub.k-1 and X.sub.k+1.
From the conditions described above, an interpolated image signal component Y.sub.p corresponding to the interpolation point X.sub.p may be represented by Formula (2) shown below. ##EQU1##
The coefficients for the image signal components Y.sub.k-1, Y.sub.k, Y.sub.k+1, and Y.sub.k+2 are referred to as the interpolation coefficients c.sub.k-1, c.sub.k, c.sub.k+1, and c.sub.k+2. These interpolation coefficients may be represented by the formulas shown below. EQU c.sub.k-1 =(-t.sup.3 +2t.sup.2 -t)/2 EQU c.sub.k =(3t.sup.3 -5t.sup.2 +2)/2 EQU c.sub.k+1 =(-3t.sup.3 +4t.sup.2 +t)/2 EQU c.sub.k =(t.sup.3 -t.sup.2)/2
As described above, it is necessary that the cubic spline interpolating function passes through the original sampling points, and that the first-order differential coefficient of the cubic spline interpolating function is continuous between adjacent sections. With the cubic spline interpolating function, the interpolation image signal for use in the reproduction of a secondary image (i.e., the image obtained from the interpolating operation), which has a comparatively high sharpness, is obtained. On the other hand, as for a portion in the original image, at which the change in density is gentle, the interpolating operation should preferably be carried out such that a secondary image, in which the sharpness is comparatively low and which is smooth, may be obtained. As the interpolating function for obtaining the interpolation image signal representing the secondary image, in which the sharpness is comparatively low and which is smooth, for example, a B spline interpolating function is known. The B spline interpolating function need not pass through the original sampling points, and it is necessary that the first-order differential coefficient and the second-order differential coefficient {represented by f"(X)} of the B spline interpolating function are continuous between adjacent sections. Specifically, in Formula (1), Formula (3) shown below obtains. ##EQU2##
Therefore, the interpolation coefficients b.sub.k-1, b.sub.k, b.sub.k+1, and b.sub.k+2, which respectively correspond to the image signal components Y.sub.k-1, Y.sub.k, Y.sub.k+1 and Y.sub.k+2, may be represented by the formulas shown below. EQU b.sub.k-1 =(-t.sup.3 +3t.sup.2 -3t+1)/6 EQU b.sub.k =(3t.sup.3 -6t.sup.2 +4)/6 EQU b.sub.k+1 =(-3t.sup.3 +3t.sup.2 +3t+1)/6 EQU b.sub.k+2 =t.sup.3 /6
The operations described above are repeated for the sections X.sub.k-2 .about.X.sub.k-1, X.sub.k-1 .about.X.sub.k, X.sub.k .about.X.sub.k+1, and X.sub.k+1 .about.X.sub.k+2. In this manner, an interpolation image signal can be obtained, which is made up of image signal components occurring at intervals different from those of the image signal components of the entire original image signal.
In this manner, in cases where a secondary image (an interpolation image) having a high sharpness is to be reproduced, for example, the cubic spline interpolating function may be used. In cases where a secondary image, which has a low sharpness and is smooth, is to be reproduced, for example, the B spline interpolating function may be used.
In U.S. Pat. No. 5,048,105, the applicant proposed an interpolation processing method for an image signal, with which the sharpness of an interpolation image can be adjusted finely by, for example, weighting the corresponding coefficients of two interpolating functions, that provide different levels of sharpness, in accordance with a desired sharpness of the interpolation image, and adding the weighted coefficients to each other. With the proposed method, for example, in cases where the cubic spline interpolating function and the B spline interpolating function are employed as the two interpolating functions, that provide different levels of sharpness, the interpolation coefficients c.sub.k-1, c.sub.k, c.sub.k+1, and c.sub.k+2 in the cubic spline interpolating function and the interpolation coefficients b.sub.k-1, b.sub.k, b.sub.k+1, and b.sub.k+2 in the B spline interpolating function, which coefficients correspond to each other and are set for the respective original image signal components Y.sub.k-1, Y.sub.k, Y.sub.k+1, and Y.sub.k+2, are weighted and added to each other. By alteration of the weighting ratio (factor) a, it is possible to obtain a secondary image having a desired level of sharpness, which is intermediate in the range from the highest sharpness (.alpha.=0) to the lowest smooth sharpness (.alpha.=1).
Specifically, weighted interpolation coefficients a.sub.k-1, a.sub.k, a.sub.k+1, and a.sub.k+2 are set as shown below. EQU a.sub.k-1 =(1-.alpha.)c.sub.k-1 +.alpha.b.sub.k-1 EQU a.sub.k =(1-.alpha.)c.sub.k +.alpha.k EQU a.sub.k+1 =(1-.alpha.)c.sub.k+1 +.alpha.b.sub.k+1 EQU a.sub.k+2 =(1-.alpha.)c.sub.k+2 +.alpha.b.sub.k+2 EQU wherein 0.ltoreq..alpha..ltoreq.1.
In accordance with the thus obtained new interpolation coefficients a.sub.k-1, a.sub.k, a.sub.k+1, and a.sub.k+2, an interpolated image signal component Y.sub.p is calculated with Formula (4) shown below. EQU Y.sub.p =a.sub.k-1 Y.sub.k-1 +a.sub.k Y.sub.k +a.sub.k+1 Y.sub.k+1 +a.sub.k+2 Y.sub.k+2 ( 4)
An actual image is composed of the picture elements arrayed in two-dimensional directions. Therefore, the interpolation coefficient a.sub.k is represented as the interpolation coefficient Bij or Cij corresponding to each of two different directions (an i direction and a j direction) of an array of picture elements in the image.
Also, in U.S. Ser. No. 08/679,830, the applicant proposed an interpolation processing method for an image signal, wherein the aforesaid weight factor a is not limited to values ranging from 0 to 1 and is set to be one of all real numbers, such that one of interpolation images having a wide variety of sharpness levels may be obtained. The interpolation images having a wide variety of sharpness levels include, for example, an interpolation image having a sharpness higher than the sharpness of the interpolation image, which is obtained from the cubic spline interpolating operation alone, and an interpolation image having a sharpness smoother than the sharpness of the interpolation image, which is obtained from the B spline interpolating operation alone.
In cases where an interpolation point is located at an image edge portion, at which the change in the image signal (e.g., the change in the image density) is sharp, such as an edge of a character pattern, it is desired that the sharp condition of the image edge portion does not become unsharp due to the interpolation processing. FIG. 4 is an explanatory graph showing how the interpolated image signal components are obtained with replication interpolation processing. In such cases, for example, as illustrated in FIG. 4, a replication interpolation method (or a nearest neighbor interpolation method) may be employed appropriately, wherein the value of the interpolated image signal component at the interpolation point is set to be identical with the original image signal value representing the picture element in the original image, which picture element is nearest to the interpolation point. The replication interpolation method, or the like, has the advantages in that the condition of the image edge portion can be retained reliably.
Therefore, processing may be carried out in the manner described below. Specifically, a threshold value processing may be carried out on a received image signal, and a judgment may thereby be made as to whether an interpolation point, for which an interpolated image signal component is to be calculated, is or is not located at an image edge portion in the original image. In cases where it is judged that the interpolation point is located at the image edge portion, the interpolated image signal component with respect to the interpolation point may be calculated with the replication interpolation method. In cases where it is judged that the interpolation point is not located at the image edge portion, the interpolation processing with the weighting of two kinds of the interpolating functions, which processing is proposed in U.S. Ser. No. 08/679,830, may be utilized with respect to the interpolation point. (As an aid in facilitating the explanation, the interpolation processing with the weighting of two kinds of the interpolating functions will hereinbelow be referred to simply as the spline interpolation processing.)
In cases where such interpolation processing is employed, a high sharpness can be kept with respect to the image edge portion. As for the other image portions, the value of the factor a described above can be altered, and a desired level of sharpness can be obtained. In this manner, an interpolation image having a desired level of sharpness can be obtained.
FIG. 8 is an explanatory graph showing a discontinuous portion occurring at a boundary between a replication interpolation processing and a spline interpolation processing. As illustrated in, for example, FIG. 8, in cases where different interpolating operation methods are employed for the image edge portion and the other image portions, the curves of the interpolating functions become discontinuous at the boundary portion, at which the applied interpolation processing is changed over (for example, between the spline interpolation processing and the replication interpolation processing) As in the image edge portion, the interpolation image signal changes sharply at the portion at which the curves of the interpolating functions are discontinuous. Therefore, the discontinuous portion is perceived as an unnatural image density change in the obtained interpolation image.
The discontinuous portion becomes particularly perceptible when the sharpness of the portions other than the image edge portion is set to be low and a smooth interpolation image is to be thereby obtained.
Specifically, in cases where the sharpness of the portions other than the image edge portion is set to be high, the aforesaid factor a serving as the weighting ratio may be set to be a real number smaller than 0. The interpolating function for the spline interpolation processing, in which the factor a is set to be a real number smaller than 0, becomes very close to the interpolating function for the replication interpolation processing. Therefore, the problems do not occur in that only the discontinuity of the interpolation image signal (image density, or the like) at the boundary between the spline interpolation processing and the replication interpolation processing becomes perceptible, and in that an unnatural feeling is thus given by the obtained interpolation image.
However, in cases where a low level of sharpness is desired for the interpolation image, the aforesaid boundary portion becomes perceptible and is reproduced as an image edge portion having a high sharpness in the interpolation image, in which the image density changes smoothly as a whole. Therefore, an interpolation image giving an unnatural feeling is obtained.